Blind Image Deconvolution using Approximate Greatest Common Divisor and Approximate Polynomial Factorisation

Images play a significant and important role in diverse areas of everyday modern life. Examples of the areas where the use of images is routine include medicine, forensic investigations, engineering applications and astronomical science. The procedures and methods that depend on image processing would benefit considerably from images that are free of blur. Most images are unfortunately affected by noise and blur that result from the practical limitations of image sourcing systems. The blurring and noise effects render the image less useful. An efficient method for image restoration is hence important for many applications. Restoration of true images from blurred images is the inverse of the naturally occurring problem of true image convolution through a blurring function. The deconvolution of images from blurred images is a non-trivial task. One challenge is that the computation of the mathematical function that represents the blurring process, which is known as the point spread function (PSF), is an ill-posed problem, i.e. an infinite number of solutions are possible for given inexact data. The blind image deconvolution (BID) problem is the central subject of this thesis. There are a number of approaches for solving the BID problem, including statistical methods and linear algebraic methods. The approach adopted in this research study for solving this problem falls within the class of linear algebraic methods. Polynomial linear algebra offers a way of computing the PSF size and its components without requiring any prior knowledge about the true image and the blurring PSF. This research study has developed a BID method for image restoration based on the approximate greatest common divisor (AGCD) algorithms, specifically, the approximate polynomial factorization (APF) algorithm of two polynomials. The developed method uses the Sylvester resultant matrix algorithm in the computation of the AGCD and the QR decomposition for computing the degree of the AGCD. It is shown that the AGCD is equal to the PSF and the deblurred image can be computed from the coprime polynomials. In practice, the PSF can be spatially variant or invariant. PSF spatial invariance means that the blurred image pixels are the convolution of the true image pixels and the same PSF. Some of the PSF bivariate functions, in particular, separable functions, can be further simplified as the multiplication of two univariate polynomials. This research study is focused on the invariant separable and non-separable PSF cases. The performance of state-of-the-art image restoration methods varies in terms of computational speed and accuracy. In addition, most of these methods require prior knowledge about the true image and the blurring function, which in a significant number of applications is an impractical requirement. The development of image restoration methods that require no prior knowledge about the true image and the blurring functions is hence desirable. Previous attempts at developing BID methods resulted in methods that have a robust performance against noise perturbations; however, their good performance is limited to blurring functions of small size. In addition, even for blurring functions of small size, these methods require the size of the blurring functions to be known and an estimate of the noise level to be present in the blurred image. The developed method has better performance than all the other state-of-the-art methods, in particular, it determines the correct size and coefficients of the PSF and then uses it to recover the original image. It does not require any prior knowledge about the PSF, which is a prerequisite for all the other methods

Deep learning-based diagnostic system for malignant liver detection

Cancer is the second most common cause of death of human beings, whereas liver cancer is the fifth most common cause of mortality. The prevention of deadly diseases in living beings requires timely, independent, accurate, and robust detection of ailment by a computer-aided diagnostic (CAD) system. Executing such intelligent CAD requires some preliminary steps, including preprocessing, attribute analysis, and identification. In recent studies, conventional techniques have been used to develop computer-aided diagnosis algorithms. However, such traditional methods could immensely affect the structural properties of processed images with inconsistent performance due to variable shape and size of region-of-interest. Moreover, the unavailability of sufficient datasets makes the performance of the proposed methods doubtful for commercial use. To address these limitations, I propose novel methodologies in this dissertation. First, I modified a generative adversarial network to perform deblurring and contrast adjustment on computed tomography (CT) scans. Second, I designed a deep neural network with a novel loss function for fully automatic precise segmentation of liver and lesions from CT scans. Third, I developed a multi-modal deep neural network to integrate pathological data with imaging data to perform computer-aided diagnosis for malignant liver detection. The dissertation starts with background information that discusses the proposed study objectives and the workflow. Afterward, Chapter 2 reviews a general schematic for developing a computer-aided algorithm, including image acquisition techniques, preprocessing steps, feature extraction approaches, and machine learning-based prediction methods. The first study proposed in Chapter 3 discusses blurred images and their possible effects on classification. A novel multi-scale GAN network with residual image learning is proposed to deblur images. The second method in Chapter 4 addresses the issue of low-contrast CT scan images. A multi-level GAN is utilized to enhance images with well-contrast regions. Thus, the enhanced images improve the cancer diagnosis performance. Chapter 5 proposes a deep neural network for the segmentation of liver and lesions from abdominal CT scan images. A modified Unet with a novel loss function can precisely segment minute lesions. Similarly, Chapter 6 introduces a multi-modal approach for liver cancer variants diagnosis. The pathological data are integrated with CT scan images to diagnose liver cancer variants. In summary, this dissertation presents novel algorithms for preprocessing and disease detection. Furthermore, the comparative analysis validates the effectiveness of proposed methods in computer-aided diagnosis

Non-ideal iris recognition

Of the many biometrics that exist, iris recognition is finding more attention than any other due to its potential for improved accuracy, permanence, and acceptance. Current iris recognition systems operate on frontal view images of good quality. Due to the small area of the iris, user co-operation is required. In this work, a new system capable of processing iris images which are not necessarily in frontal view is described. This overcomes one of the major hurdles with current iris recognition systems and enhances user convenience and accuracy. The proposed system is designed to operate in two steps: (i) preprocessing and estimation of the gaze direction and (ii) processing and encoding of the rotated iris image. Two objective functions are used to estimate the gaze direction. Later, the off-angle iris image undergoes geometric transformations involving the estimated angle and is further processed as if it were a frontal view image. Two methods: (i) PCA and (ii) ICA are used for encoding. Three different datasets are used to quantify performance of the proposed non-ideal recognition system

Non-Standard Imaging Techniques

The first objective of the thesis is to investigate the problem of reconstructing a small-scale object (a few millimeters or smaller) in 3D. In Chapter 3, we show how this problem can be solved effectively by a new multifocus multiview 3D reconstruction procedure which includes a new Fixed-Lens multifocus image capture and a calibrated image registration technique using analytic homography transformation. The experimental results using the real and synthetic images demonstrate the effectiveness of the proposed solutions by showing that both the fixed-lens image capture and multifocus stacking with calibrated image alignment significantly reduce the errors in the camera poses and produce more complete 3D reconstructed models as compared with those by the conventional moving lens image capture and multifocus stacking. The second objective of the thesis is modelling the dual-pixel (DP) camera. In Chapter 4, to understand the potential of the DP sensor for computer vision applications, we study the formation of the DP pair which links the blur and the depth information. A mathematical DP model is proposed which can benefit depth estimation by the blur. These explorations motivate us to propose an end-to-end DDDNet (DP-based Depth and Deblur Network) to jointly estimate the depth and restore the image . Moreover, we define a reblur loss, which reflects the relationship of the DP image formation process with depth information, to regularize our depth estimate in training. To meet the requirement of a large amount of data for learning, we propose the first DP image simulator which allows us to create datasets with DP pairs from any existing RGBD dataset. As a side contribution, we collect a real dataset for further research. Extensive experimental evaluation on both synthetic and real datasets shows that our approach achieves competitive performance compared to state-of-the-art approaches. Another (third) objective of this thesis is to tackle the multifocus image fusion problem, particularly for long multifocus image sequences. Multifocus image stacking/fusion produces an in-focus image of a scene from a number of partially focused images of that scene in order to extend the depth of field. One of the limitations of the current state of the art multifocus fusion methods is not considering image registration/alignment before fusion. Consequently, fusing unregistered multifocus images produces an in-focus image containing misalignment artefacts. In Chapter 5, we propose image registration by projective transformation before fusion to remove the misalignment artefacts. We also propose a method based on 3D deconvolution to retrieve the in-focus image by formulating the multifocus image fusion problem as a 3D deconvolution problem. The proposed method achieves superior performance compared to the state of the art methods. It is also shown that, the proposed projective transformation for image registration can improve the quality of the fused images. Moreover, we implement a multifocus simulator to generate synthetic multifocus data from any RGB-D dataset. The fourth objective of this thesis is to explore new ways to detect the polarization state of light. To achieve the objective, in Chapter 6, we investigate a new optical filter namely optical rotation filter for detecting the polarization state with a fewer number of images. The proposed method can estimate polarization state using two images, one with the filter and another without. The accuracy of estimating the polarization parameters using the proposed method is almost similar to that of the existing state of the art method. In addition, the feasibility of detecting the polarization state using only one RGB image captured with the optical rotation filter is also demonstrated by estimating the image without the filter from the image with the filter using a generative adversarial network